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SUBROUTINE DGSVTS( M, P, N, A, AF, LDA, B, BF, LDB, U, LDU, V,
$ LDV, Q, LDQ, ALPHA, BETA, R, LDR, IWORK, WORK,
$ LWORK, RWORK, RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* June 30, 1999
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LDQ, LDR, LDU, LDV, LWORK, M, N, P
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), ALPHA( * ),
$ B( LDB, * ), BETA( * ), BF( LDB, * ),
$ Q( LDQ, * ), R( LDR, * ), RESULT( 6 ),
$ RWORK( * ), U( LDU, * ), V( LDV, * ),
$ WORK( LWORK )
* ..
*
* Purpose
* =======
*
* DGSVTS tests DGGSVD, which computes the GSVD of an M-by-N matrix A
* and a P-by-N matrix B:
* U'*A*Q = D1*R and V'*B*Q = D2*R.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* P (input) INTEGER
* The number of rows of the matrix B. P >= 0.
*
* N (input) INTEGER
* The number of columns of the matrices A and B. N >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,M)
* The M-by-N matrix A.
*
* AF (output) DOUBLE PRECISION array, dimension (LDA,N)
* Details of the GSVD of A and B, as returned by DGGSVD,
* see DGGSVD for further details.
*
* LDA (input) INTEGER
* The leading dimension of the arrays A and AF.
* LDA >= max( 1,M ).
*
* B (input) DOUBLE PRECISION array, dimension (LDB,P)
* On entry, the P-by-N matrix B.
*
* BF (output) DOUBLE PRECISION array, dimension (LDB,N)
* Details of the GSVD of A and B, as returned by DGGSVD,
* see DGGSVD for further details.
*
* LDB (input) INTEGER
* The leading dimension of the arrays B and BF.
* LDB >= max(1,P).
*
* U (output) DOUBLE PRECISION array, dimension(LDU,M)
* The M by M orthogonal matrix U.
*
* LDU (input) INTEGER
* The leading dimension of the array U. LDU >= max(1,M).
*
* V (output) DOUBLE PRECISION array, dimension(LDV,M)
* The P by P orthogonal matrix V.
*
* LDV (input) INTEGER
* The leading dimension of the array V. LDV >= max(1,P).
*
* Q (output) DOUBLE PRECISION array, dimension(LDQ,N)
* The N by N orthogonal matrix Q.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= max(1,N).
*
* ALPHA (output) DOUBLE PRECISION array, dimension (N)
* BETA (output) DOUBLE PRECISION array, dimension (N)
* The generalized singular value pairs of A and B, the
* ``diagonal'' matrices D1 and D2 are constructed from
* ALPHA and BETA, see subroutine DGGSVD for details.
*
* R (output) DOUBLE PRECISION array, dimension(LDQ,N)
* The upper triangular matrix R.
*
* LDR (input) INTEGER
* The leading dimension of the array R. LDR >= max(1,N).
*
* IWORK (workspace) INTEGER array, dimension (N)
*
* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The dimension of the array WORK,
* LWORK >= max(M,P,N)*max(M,P,N).
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,P,N))
*
* RESULT (output) DOUBLE PRECISION array, dimension (6)
* The test ratios:
* RESULT(1) = norm( U'*A*Q - D1*R ) / ( MAX(M,N)*norm(A)*ULP)
* RESULT(2) = norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP)
* RESULT(3) = norm( I - U'*U ) / ( M*ULP )
* RESULT(4) = norm( I - V'*V ) / ( P*ULP )
* RESULT(5) = norm( I - Q'*Q ) / ( N*ULP )
* RESULT(6) = 0 if ALPHA is in decreasing order;
* = ULPINV otherwise.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J, K, L
DOUBLE PRECISION ANORM, BNORM, RESID, TEMP, ULP, ULPINV, UNFL
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
EXTERNAL DLAMCH, DLANGE, DLANSY
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMM, DGGSVD, DLACPY, DLASET, DSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
ULP = DLAMCH( 'Precision' )
ULPINV = ONE / ULP
UNFL = DLAMCH( 'Safe minimum' )
*
* Copy the matrix A to the array AF.
*
CALL DLACPY( 'Full', M, N, A, LDA, AF, LDA )
CALL DLACPY( 'Full', P, N, B, LDB, BF, LDB )
*
ANORM = MAX( DLANGE( '1', M, N, A, LDA, RWORK ), UNFL )
BNORM = MAX( DLANGE( '1', P, N, B, LDB, RWORK ), UNFL )
*
* Factorize the matrices A and B in the arrays AF and BF.
*
CALL DGGSVD( 'U', 'V', 'Q', M, N, P, K, L, AF, LDA, BF, LDB,
$ ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, IWORK,
$ INFO )
*
* Copy R
*
DO 20 I = 1, MIN( K+L, M )
DO 10 J = I, K + L
R( I, J ) = AF( I, N-K-L+J )
10 CONTINUE
20 CONTINUE
*
IF( M-K-L.LT.0 ) THEN
DO 40 I = M + 1, K + L
DO 30 J = I, K + L
R( I, J ) = BF( I-K, N-K-L+J )
30 CONTINUE
40 CONTINUE
END IF
*
* Compute A:= U'*A*Q - D1*R
*
CALL DGEMM( 'No transpose', 'No transpose', M, N, N, ONE, A, LDA,
$ Q, LDQ, ZERO, WORK, LDA )
*
CALL DGEMM( 'Transpose', 'No transpose', M, N, M, ONE, U, LDU,
$ WORK, LDA, ZERO, A, LDA )
*
DO 60 I = 1, K
DO 50 J = I, K + L
A( I, N-K-L+J ) = A( I, N-K-L+J ) - R( I, J )
50 CONTINUE
60 CONTINUE
*
DO 80 I = K + 1, MIN( K+L, M )
DO 70 J = I, K + L
A( I, N-K-L+J ) = A( I, N-K-L+J ) - ALPHA( I )*R( I, J )
70 CONTINUE
80 CONTINUE
*
* Compute norm( U'*A*Q - D1*R ) / ( MAX(1,M,N)*norm(A)*ULP ) .
*
RESID = DLANGE( '1', M, N, A, LDA, RWORK )
*
IF( ANORM.GT.ZERO ) THEN
RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M, N ) ) ) / ANORM ) /
$ ULP
ELSE
RESULT( 1 ) = ZERO
END IF
*
* Compute B := V'*B*Q - D2*R
*
CALL DGEMM( 'No transpose', 'No transpose', P, N, N, ONE, B, LDB,
$ Q, LDQ, ZERO, WORK, LDB )
*
CALL DGEMM( 'Transpose', 'No transpose', P, N, P, ONE, V, LDV,
$ WORK, LDB, ZERO, B, LDB )
*
DO 100 I = 1, L
DO 90 J = I, L
B( I, N-L+J ) = B( I, N-L+J ) - BETA( K+I )*R( K+I, K+J )
90 CONTINUE
100 CONTINUE
*
* Compute norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP ) .
*
RESID = DLANGE( '1', P, N, B, LDB, RWORK )
IF( BNORM.GT.ZERO ) THEN
RESULT( 2 ) = ( ( RESID / DBLE( MAX( 1, P, N ) ) ) / BNORM ) /
$ ULP
ELSE
RESULT( 2 ) = ZERO
END IF
*
* Compute I - U'*U
*
CALL DLASET( 'Full', M, M, ZERO, ONE, WORK, LDQ )
CALL DSYRK( 'Upper', 'Transpose', M, M, -ONE, U, LDU, ONE, WORK,
$ LDU )
*
* Compute norm( I - U'*U ) / ( M * ULP ) .
*
RESID = DLANSY( '1', 'Upper', M, WORK, LDU, RWORK )
RESULT( 3 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / ULP
*
* Compute I - V'*V
*
CALL DLASET( 'Full', P, P, ZERO, ONE, WORK, LDV )
CALL DSYRK( 'Upper', 'Transpose', P, P, -ONE, V, LDV, ONE, WORK,
$ LDV )
*
* Compute norm( I - V'*V ) / ( P * ULP ) .
*
RESID = DLANSY( '1', 'Upper', P, WORK, LDV, RWORK )
RESULT( 4 ) = ( RESID / DBLE( MAX( 1, P ) ) ) / ULP
*
* Compute I - Q'*Q
*
CALL DLASET( 'Full', N, N, ZERO, ONE, WORK, LDQ )
CALL DSYRK( 'Upper', 'Transpose', N, N, -ONE, Q, LDQ, ONE, WORK,
$ LDQ )
*
* Compute norm( I - Q'*Q ) / ( N * ULP ) .
*
RESID = DLANSY( '1', 'Upper', N, WORK, LDQ, RWORK )
RESULT( 5 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / ULP
*
* Check sorting
*
CALL DCOPY( N, ALPHA, 1, WORK, 1 )
DO 110 I = K + 1, MIN( K+L, M )
J = IWORK( I )
IF( I.NE.J ) THEN
TEMP = WORK( I )
WORK( I ) = WORK( J )
WORK( J ) = TEMP
END IF
110 CONTINUE
*
RESULT( 6 ) = ZERO
DO 120 I = K + 1, MIN( K+L, M ) - 1
IF( WORK( I ).LT.WORK( I+1 ) )
$ RESULT( 6 ) = ULPINV
120 CONTINUE
*
RETURN
*
* End of DGSVTS
*
END
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